polar coordinates ,cartesian/rectangular coordinates

Question

Answer 1

Step 1 :

Conversion from polar coordinates to rectangular co-ordinates :

If P is a point with polar coordinates , the rectangular coordinates of P are given by

and .

Step 2 :

(2)

(a)

The point  is 

Conversion to rectangular coordinates :

Substitute and in x.

Substitute and in y.

The point in rectangular coordinates is

Step 3 :

(b) 

The point is 

Conversion to rectangular coordinates :

Substitute and in x.

Substitute and in y.

The point in rectangular coordinates is

Step 4 :

(c)

The point is 

Conversion to rectangular coordinates :

Substitute and in x.

Substitute and in y.

The point in rectangular coordinates is

Solution :

(a) The point in rectangular coordinates is

(b) The point in rectangular coordinates is

(c) The point in rectangular coordinates is

Answer 2

Step 1 :

Conversion from rectangular coordinates to polar co-ordinates :

If P  is a point with rectangular coordinates , the polar coordinates of P are given by and

Step 2 :

(3)

(a)

The point is

Conversion to polar coordinates :

Substitute and in r.

Substitute and in .

The point in polar coordinates is 

Step 3 :

(b)

The point is

Conversion to polar coordinates :

Substitute and in r.

Substitute and in .

Since the point lies in fourth quadrant, take the angle

The point in polar coordinates is

Solution :

(a) The point in polar coordinates is 

(b) The point in polar coordinates is